Express the vector as a product of its length and direction.
--5i + 5j + 5k
A) $5 \sqrt { 3 } \left( - \frac { \sqrt { 3 } } { 3 } \mathbf { i } + \frac { \sqrt { 3 } } { 3 } \mathbf { j } + \frac { \sqrt { 3 } } { 3 } \mathbf { k } \right)$
B) $\frac { \sqrt { 3 } } { 15 } \left( - \frac { \sqrt { 3 } } { 3 } \mathbf { i } + \frac { \sqrt { 3 } } { 3 } \mathbf { j } + \frac { \sqrt { 3 } } { 3 } \mathbf { k } \right)$
C) $5 \sqrt { 3 } \left( - \frac { 1 } { 75 } \mathbf { i } + \frac { 1 } { 75 } \mathbf { j } + \frac { 1 } { 75 } \mathbf { k } \right)$
D) $5 ( - \mathbf { i } + \mathbf { j } + \mathbf { k } )$

Question

Express the vector as a product of its length and direction.
--5i + 5j + 5k 
A) $5 \sqrt { 3 } \left( - \frac { \sqrt { 3 } } { 3 } \mathbf { i } + \frac { \sqrt { 3 } } { 3 } \mathbf { j } + \frac { \sqrt { 3 } } { 3 } \mathbf { k } \right)$
B) $\frac { \sqrt { 3 } } { 15 } \left( - \frac { \sqrt { 3 } } { 3 } \mathbf { i } + \frac { \sqrt { 3 } } { 3 } \mathbf { j } + \frac { \sqrt { 3 } } { 3 } \mathbf { k } \right)$
C) $5 \sqrt { 3 } \left( - \frac { 1 } { 75 } \mathbf { i } + \frac { 1 } { 75 } \mathbf { j } + \frac { 1 } { 75 } \mathbf { k } \right)$
D) $5 ( - \mathbf { i } + \mathbf { j } + \mathbf { k } )$

Quizplus · Accepted Answer

The length of the vector is calculated as $\sqrt{(-5)^2 + 5^2 + 5^2} = 5\sqrt{3}$. The direction is obtained by dividing each component by the length, resulting in $\left( - \frac { \sqrt { 3 } } { 3 } \mathbf { i } + \frac { \sqrt { 3 } } { 3 } \mathbf { j } + \frac { \sqrt { 3 } } { 3 } \mathbf { k } \right)$.

Express the Vector as a Product of Its Length and Direction